10.30am: Today marks the one month anniversary of Occupy Wall Street. The initial group occupied Zuccotti Park on 17 September, and since then the demonstrators marches and near-removal have kept them in the public eye.

Saturday marked Occupy Wall Street's biggest day of action so far, with up to 20,000 gathering in Times Square at 5pm. Streets were blocked off and protesters contained behind barriers as they chanted anti-corporate messages, while police deployed officers on horseback and arrested 70 people during the day.

The action later spread to Washington Square Park, some 30 blocks south of Times Square, where a spontaneous occupation was discussed, decided upon and then dispersed by police, who arrested around 10 would-be occupiers.

Protests inspired by the Occupy Wall Street movement in New York and the "Indignants" in Spain have spread to cities around the world.

Tens of thousands went on the march in New York, London, Frankfurt, Madrid, Rome, Sydney and Hong Kong as organisers aimed to "initiate global change" against capitalism and austerity measures.

There were extraordinary scenes in New York where at least 10,000 protesters took their message from the outpost of Zuccotti Park into the heart of the city, thronging into Times Square.

Only 36 hours earlier, police were preparing to evict the protest from Zuccotti Park. On Saturday they escorted thousands of marchers all day as they made their way uptown through Manhattan, and looked on as they held a rally at a New York landmark.

We'll have the latest news and developments on Occupy Wall Street and other occupations around the world, as protesters celebrate having spent one month in Zuccotti Park. Have your say by leaving a comment below or tweeting me @AdamGabbatt

10.51am: Karen McVeigh writes that a bid is underway to help those arrested for their involvement in OWS prostests avoid prosecutions:

Graham Turner/Guardian

Lawyers representing hundreds of Occupy Wall Street protesters arrested over the last few weeks are demanding that prosecutors drop the charges. They say if not, they will insist on going to trial, putting pressure on Manhattan's busy criminal courts.

Members of the rights group, the National Lawyers Guild, plan to meet with prosecutors from Manhattan's District Attorney's office today to set out their position.

Defence lawyer Martin Stolar told the Daily News: "I'd like to suggests to the DA's office the appropriate way to deal with these cases is outright dismissal."

First-time offenders on minor crimes are generally offered an "adjournment in contemplation of dismissal", where charges are dismissed after six months if the offender is not re-arrested.

11.19am: Some 175 people were arrested in Chicago at the weekend after attempting to expand their occupation from the city's financial district to Grant Park. Undeterred, however, demonstrators are planning a march in the city today.

A permit is required for staying overnight in the park, and organizers admitted to not seeking a permit. The demonstrators say they refused repeated orders from police to leave.

Those arrested were held in police custody overnight but were released a few hours later.

"The Chicago Police Department handled it in a very professional manner. They were courteous. We were given multiple warnings of what was going to take place," said Andrew Smith, who was arrested.

Many of those arrested are returned Sunday night for another march and rally. Once again, they repeated their message against corporate greed in the face of high unemployment and home foreclosures.

The news channel said the Occupy Chicago movement has since spread to other parts of Illinois, including Peoria and Springfield, where "hundreds chanted and marched through downtown streets".

Occupy Chicago's home base continues to be Chicago's financial district. Meanwhile, organizers say they will start a daily meeting in Grant Park.

The Chicago Tribune said police used the attempted occupation as "a trial run" for dealing with the two international summits, and the expected protests around them, which are coming to Chicago next year. Unlike some of the policing in New York, however, it seems the demonstration on Saturday night was quelled in a peaceful manner:

It also would set a bad precedent for dealing with thousands of demonstrators expected to converge on Chicago from around the world during the G-8 and NATO summits that will be held simultaneously in May, the source said.

The arrests were a stark contrast to the clash that occurred in New York two weeks ago when nearly 700 protesters were arrested on the Brooklyn Bridge.

Chicago police maintained open lines of communication with the group throughout the protest and extended ample time and opportunity for the group to leave the park, said Lt. Maureen Biggane, a police spokeswoman. The group largely complied, she said.

11.44am: This map from the website map.15october.net shows how widely demonstrations spread across the world on 15 October.

United for #globalchange map of all 15 October action Photograph: United for #globalchange United for #globalchange/Public Domain

It was compiled by gathering details of occupations and protests from people tweeting #event15oct. Impressive.

12.10pm:The Washington Post reports that Occupy Wall Street has raised some $300,000 in cash through website donations and visitors to the park.

The movement has an account at Amalgamated Bank, which bills itself as "the only 100 percent union-owned bank in the United States."

Donated goods ranging from blankets and sleeping bags to cans of food and medical and hygienic supplies are being stored in a cavernous space donated by the United Federation of Teachers, which has offices in the building a block from Wall Street near the private park protesters occupy.

Among the items are 20 pairs of swimming goggles (to shield protesters from pepper-spray attacks). Supporters are shipping about 300 boxes a day, many with notes and letters, Strekal said.

"Some are heartwrenching, beautiful," and come from people who have lost jobs and houses, he said. "So they send what they can, even if it's small."

Strekal said donated goods, stored for a "long-term occupation," have been used to create "Jail Support" kits consisting of a blanket, a granola bar and sanitary wipes for arrested protesters to receive when they are freed.

12.34pm: UN Secretary-General Ban Ki-moon has said he understands the occupy movement, according to an Associated Press report:

Ban told reporters during a visit to Switzerland that the finance chiefs from the Group of 20 rich and developing nations should listen to the people and come up with "actionable plans" to fix the problems.

"Business as usual, or just looking at their own internal economic issues, will not give any answers to a very serious international economic crisis," Ban said, as G-20 talks were being held in Paris.

"That is what you are seeing all around the world, starting from Wall Street, people are showing their frustrations, are trying to send a very clear and unambiguous message around the world," he said.

12.53pm: President Barack Obama will seek to tap into public anger at Wall Street excess, Reuters reported today. Obama previously said he understood the frustration of protesters, but his spokesman has gone further today, using the '99 percent' terminology of Occupy Wall Street demonstrators.

From Reuters:

"The president will continue to acknowledge the frustration that he himself shares about the need for Washington to do more to support our economic recovery and to ensure that the interest of the 99 percent of Americans is well-represented," spokesman Josh Earnest said when asked whether Obama would offer a message for Wall Street protesters on his trip south.

The Democratic president wants to step up the pressure on Republicans as he tries to push through his jobs package piece by piece, starting this week after his full plan went down to defeat in Congress last week.

With election races looming, Obama's strategy is to force Republicans to give ground or be painted as obstructionists more interested in shielding "millionaires and billionaires" - "the 1 percent" - from paying their fair share of taxes.

Republicans say Obama's original package was laden with wasteful spending and job-killing tax hikes for wealthy Americans. They have accused him of demonizing them and promoting "class warfare" instead of working with them to find areas of agreement.In the Republicans' weekend radio address, Representative Kevin McCarthy urged Obama to "come off the campaign trail and get to work."

The deadlock over the jobs bill has raised concerns that political dysfunction in Washington will prevent any major steps to spur hiring before the November 2012 elections.

1.36pm: News of a must have download for occupy demonstrators everywhere – the "I'm getting arrested app".

I'm Getting Arrested is a creative Android app that, according to developer Quadrant 2, was inspired by a real-life "Occupy Wall Street" incident. It lets you quickly notify your family, friends, and crack legal team (if you have one) of your situation with a single tap of your finger. Just initially enter a custom message and some SMS-ready numbers to contact in the event of your arrest. Then, as you're about to be corralled into the back of a squad car, fire the app up and long-press the bull's-eye for 2 seconds. From there, you can rest assured that your message will be sent to the appropriate contacts.

Voters split 46 - 45 percent in their approval of the way police are handling the Wall Street protest, but approve 61 - 33 percent of how the police are doing their job overall.

"It's a free country. Let them keep on protesting as long as they obey the law, New Yorkers say overwhelmingly," said Maurice Carroll, director of the Quinnipiac University Polling Institute. "Critics complain that no one can figure out what the protesters are protesting. But seven out of 10 New Yorkers say they understand and most agree with the anti-Wall Street views of the protesters.

"For a while, the critics focused on the cops' use of pepper spray at the protests. Voters are divided on how police are handling the protesters, but they say almost 2-to-1 that police are doing a good job overall."

Asked who is to blame for the current state of the nation's economy;

• 37 percent of New York City voters blame the administration of former President George W. Bush;• 21 percent blame Wall Street and financial institutions;• 18 percent blame Congress;• 11 percent blame President Barack Obama.

3.10pm: Bit of a break while I head down to Zuccotti Park – will file more from the scene.

5.39pm: While we wait for Adam to file from Zuccotti, this is Matt Wells taking over with some more OWS updates, including news from the Gothamist website on the hipster cop who's found some fame in the past few days.

New York 'hipster cop' on duty at the Occupy Wall Street march.
Photograph: @mtracey @mtracey/Public Domain

The website reports that community affairs detective Rick Lee rides a bike, approves of bike lanes, but doesn't ride fixed gear. He eats organic food, and is far from the typical coffee-and-donut NYPD officer.

5.43pm: My colleague Karen McVeigh reports that a formal investigation has been launched into another NYPD officer over conduct at an Occupy Wall Street demonstration. Here's the opening to her report:

Graham Turner/Guardian

A second senior New York police officer is being formally investigated over allegations that he assaulted an Occupy Wall Street protester, raising fresh questions over the NYPD's deployment of supervisors on the front line in volatile public order situations.

The officer, who has been named in news reports as deputy inspector Johnny Cardona, was filmed on Friday grabbing the protester from behind, spinning him round and appearing to punch him in the face so hard that he fell to the ground.

The New York Civilian Complaint Review Board, an independent mayoral agency that deals with allegations of excessive or unnecessary force against police, is now investigating the incident, along with a number of other complaints over policing of the protests.

6.30pm: Adam again here – it's pretty quiet down at Zuccotti Park this afternoon, the usual throng of tourists meandering through and taking photos while occupiers work on various aspects of camp life – some preparing food, some creating signs, others engaged in working group meetings while some sleep.